Direct computation of functions using low-complexity algorithms can be applied both for hardware constraints and in systems where storage capacity is a challenge for processing a large volume of data. We present improved algorithms for fast calculation of the inverse square root function for single-precision and double-precision floating-point numbers. Higher precision is also discussed. Our approach consists in minimizing maximal errors by finding optimal magic constants and modifying the Newton-Raphson coefficients. The obtained algorithms are much more accurate than the original fast inverse square root algorithm and have similar very low computational costs.

中文翻译：

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通过修改 Newton-Raphson 校正来提高快速平方根的精度

使用低复杂度算法的函数直接计算既适用于硬件约束，也适用于存储容量对处理大量数据构成挑战的系统。我们提出了用于快速计算单精度和双精度浮点数的平方根反比函数的改进算法。还讨论了更高的精度。我们的方法包括通过找到最佳魔术常数和修改 Newton-Raphson 系数来最小化最大误差。得到的算法比原来的快速平方根反算法精确得多，并且具有类似的非常低的计算成本。